Molecular Features Behind Formation of α or β Co-Crystalline and Nanoporous-Crystalline Phases of PPO

Guest molecular features determining the formation of α and β phases of poly(2-6-dimethyl-1,4-phenylene) oxide (PPO) are explored by collecting literature data and adding many new film preparations, both by solution casting and by guest sorption in amorphous films. Independently of the considered preparation method, the α-form is favored by the hydrophobic and bulky guest molecules, while the hydrophilic and small guest molecules favor the β-form. Furthermore, molecular modeling studies indicate that the β-form inducer guests establish stronger dispersive interactions with the PPO units than the α-form inducer guests. Thus, the achievement of co-crystalline (and derived nanoporous crystalline) α- and β-forms would result from differences in energy gain due to the host–guest interactions established at the local scale.

In particular, two completely different classes of co-crystalline (CC) forms with low-molecularmass guest molecules can be obtained. The CC forms of Class i are formed only with a few specific guests (α-pinene, tetralin, and decalin), exhibit regular polymer helices, and give rise to highly ordered crystalline phases (Barrales-Rienda and Fatou, 1971;Horikiri, 1972;Hurek and Turska, 1984;Tarallo et al., 2012). The CC forms of Class ii are instead formed with many guests and exhibit a different chain conformations and less ordered crystalline phases (Daniel et al., 2011;Nagendra et al., 2019;Golla et al., 2020a;Alentiev et al., 2021).
Both the CC αand β-forms can be obtained by guest-induced crystallization of amorphous samples or solution processing. However, in previous studies, we have found that most guest molecules give only CC α-form or CC β-form, independently of the crystallization procedure, and, as a consequence, have been named α or β guests of PPO.
After guest removal, the CC phases of Class i become amorphous (Barrales-Rienda and Fatou, 1971;Horikiri, 1972;Hurek and Turska, 1984;Tarallo et al., 2012), while the CC phases of Class ii can produce two different nanoporous crystalline (NC) forms, i.e., crystalline forms with a density lower than that of the corresponding amorphous phase. These NC forms were also named α and β because they maintain wide-angle x-ray diffraction (WAXD) patterns similar to those of the corresponding CC forms (Nagendra et al., 2019). The NC αand β-forms exhibit crystalline densities of nearly 0.93 and 0.95 g/ cm 3 , respectively, being much lower than that of the corresponding amorphous phase (1.04 g/cm 3 ) (Daniel et al., 2011;Nagendra et al., 2019).
A study on the stability of the NC αand β-forms to the uptake of β and α guests, respectively, has shown that the NC α phases by sorption of a β guest lead to CC α phases, while on the contrary, the NC β phases by sorption of an α guest can lead to CC α phases (Nagendra et al., 2020). This clearly indicates a higher thermodynamic stability of the CC α phases (Nagendra et al., 2020). A recent study has also shown that NC α phases have generally higher melting temperatures with respect to NC β phases (Nagendra et al., 2021a).
The present study collects literature data as well as new data relative to the influence of the chemical nature of the guest on the formation of CC and NC α or β phases of PPO. PPO crystallization is conducted by two different routes: solution casting and guest-induced crystallization of amorphous films. The aim is to try to establish, with the support of molecular modeling, guest molecular features determining the formation of α or β crystalline phases.
Amorphous PPO films were obtained by casting at 60°C of a 1.5 wt% chloroform solution. CC PPO films were prepared by immersion of amorphous PPO films in the liquid guest at room temperature, and this method is indicated in Table 1 as guestinduced crystallization (GIC). Most CC PPO films were also obtained by casting of 1.5 wt% polymer solutions, and this method is indicated in Table 1 as casting. NC films were obtained by room temperature sorption/desorption treatment of CC films with acetonitrile, which is a very volatile guest of cocrystalline phases of PPO. Film thickness is generally in the range of 40-70 µm.
X-ray diffraction patterns were obtained by a Bruker D2 automatic diffractometer with nickel-filtered CuKα radiation, operated at a step size of 0.03°with 164 s/step.
Fourier transform infrared spectroscopy (FTIR) was conducted with a Vertex 70 Bruker spectrophotometer. It is equipped with a deuterated triglycine sulfate detector and a Ge/KBr beam splitter, which are operated at 2.0 cm −1 resolution. A total of 32 scans were averaged to reduce the spectral noise.
The guest molecular volume was calculated from the following equation (Nagendra et al., 2021b): where M and ρ are the molecular mass and density of the guest molecules, respectively. N A is the Avogadro's number (6.02 × 10 23 molecules/mol). We carried out the density functional theory static calculations with the Gaussian 09, Revision E.01 set of programs (Frisch et al., 2016). We adopted the B3LYP functional (Perdew, 1986;Becke, 1988) opportunely corrected with the dispersion term, keyword Empirical Dispersion = GD3BJ in the used package (Grimme, 2004;Grimme et al., 2004). All the atoms (C, H, O, and Cl) were electronically described with the standard split-valence basis set with a polarization function of Ahlrichs and co-workers (Schäfer et al., 1992), keyword SVP in Gaussian 09 E.01.

RESULTS AND DISCUSSION
3.1 Guests Leading to α and β Crystalline Forms WAXD patterns of the NC PPO films (with thickness in the range 40-70 µm), as obtained by casting from 1.5 wt% polymer solutions in many different solvents, followed by guest removal by immersion in acetonitrile for 2 hours, are shown in Figure 1. The patterns of Figure 1 clearly show that the crystalline phases obtained from the polymer solutions in p-xylene (A) and 1,3-dichlorobenzene (B) exhibit hk0 diffraction peaks at 2θ CuKα ≈ 7.1°, 11.3°, 15.0°typical of the αform, while the crystalline phases obtained with perchloroethylene (D), ethylbenzene (E), 1,2-dichloropropane (F), and 1,4-dioxane (G) exhibit the hk0 diffraction peaks at 2θ CuKα ≈ 7.7°, 12.8°typical of the β-form. The WAXD pattern of the film obtained by casting from m-xylene solution (C) shows diffraction peaks of both α and β crystalline forms. This information is confirmed by FTIR spectra of the same films of Figure 1, which are reported in Figure 2, for the spectral range 800-400 cm −1 . In fact, Figures 2A,B show absorbance peaks typical of the α-form (at 773 and 414 cm −1 ), while the spectra of Figures 2D-G show absorbance peaks typical of the βform (at 777 and 419 cm −1 ).
The crystalline forms (α or β) of films as crystallized by sorption of the same solvents in amorphous PPO films were also established by WAXD and FTIR measurements, like those of Figures 1, 2, respectively.
Table 1 collects in its last column the crystalline forms (α or β) of all films characterized in this study together with those already reported in the literature (Khulbe et al., 2000;Daniel et al., 2011;Nagendra et al., 2019;Golla et al., 2020b;Nagendra et al., 2021a;Nagendra et al., 2021b). In Table 1, the guest molecules are ordered on the basis of their solubility parameter (second column) while the used crystallization methods are indicated in the fourth column.
This fourth column of Table 1 clearly shows that the structure of the obtained crystalline forms does not depend on the crystallization method but only on the chemical nature of the guest used for polymer co-crystallization. Moreover, Table 1 shows the absence of any correlation between the structure of the CC forms (α or β) and the solubility parameter of the guest, which is generally expected to be relevant for host-guest cocrystallizations.
Based on the crystallization data of Table 1, we have explored possible correlations between the structural and physical properties of the considered guests and achievement of the αand β-forms. We found the best correlations with molecular volume and solubility in water, as shown in Tables 2, 3, respectively.
In detail, Table 2 shows that all the considered guests with molecular volumes higher than 230 Å 3 and lower than 149 Å 3 lead to the αand β-forms, respectively. As for the guest molecular volume, it is worth adding that it also has a key role in determining the orientation (with crystalline chain axis being preferentially parallel or perpendicular to the film plane) (Rizzo et al., 2019b) of PPO films (Nagendra et al., 2021b). Table 3 shows that all guests whose solubility is lower than 0.11 mmol per 100 ml of water and higher than 2 mmol per 100 ml of water lead to the αand β-forms, respectively. In summary, our data in Tables 1-3 show that, independently of the crystallization method, the α-form is favored by hydrophobic and bulky guest molecules while the hydrophilic and small guest molecules favor the β-form. Hence, more hydrophilic and smaller guest molecules favor the formation of the CC and NC crystalline β-forms, which are characterized by a higher chain periodicity (Nagendra et al., 2019).
The molecular modeling of the following section is aimed to rationalize the presently observed behavior.

Energy Evaluations Associated With the Interactions of Guest Molecules With PPO Units
Potential energy calculations were performed in the hypothesis that the formation of the α and β CC and NC forms is driven by the host-guest dispersive interactions exerted at the local scale between a PPO monomeric unit and a guest molecule. In particular, the potential energy was calculated on the methylterminated model dimer of PPO as shown in Figure 3B, in the absence and presence of four kinds of probe molecules, namely 1,2-dichloroethane (DCA) and CHCl 3 , as examples of β-form inducer guests, and 1,1,1-trichloroethane (TCA) and CCl 4 , as examples of α-form inducer guests. For the sake of simplicity, the conformation of the model dimer was assumed in the extended state as in the repetition unit of the model chain of Supplementary Figure S2C of Nagendra et al. (2019). In the calculation, the model dimer was gradually stretched through deformation of the valence angle at the central Oc atom Cph-Oc-Cph (τ) (C and ph standing for central oxygen atom and carbon phenyl rings, respectively) over a range of values between 119 and 140° ( Naumov and Ziatdinova, 1984;Baukova et al., 1994a;Baukova et al., 1994b;Nevalainen and Rissanen, 1994). The stretching state of the model dimer is measured by the increase of the end-to-end distance d e-to-e with an increase of τ as reported in Supplementary Table S1.
In the first step, calculations were performed on the isolated guest, and the isolated model dimer as a function of τ, to find the    Figure 3B. For each value of τ, the energy gain (ΔE) is calculated as the difference between the minimized potential energy of the adduct (guest + stretched model dimer) E a-st with stretched model dimer and the sum of the potential energy of the isolated guest (E g ) and of the isolated model dimer with τ deformed to the same value of the adduct (E d-st ), that is,  Figure S1 as a function of τ ( Figure 3B). It is apparent that the potential energy is almost constant for τ lower than 125°, then it gradually increases with an increase of the stretching state of the dimer. In the second step, the most suitable relative positioning of the guest molecules with respect to the PPO model dimer to be used for initializing the minimization procedure was found through a trialand-error process, by manually changing the relative arrangement of the host-guest pair (adduct), while treating the model dimer and the guest in low-energy conformations as rigid bodies. In practice, the guest was initially positioned with the center of mass cm g (g standing for guest) pointing perpendicular to the plane of the phenyl ring in front of the corresponding center of mass cm 1 ( Figure 3B) and/or perpendicular to the end-to-end segment d e-to-e along the direction crossing Oc ( Figure 3B). The space of configurations was then sampled by casually rotating the guest around its principal axes and, for the configurations directed with cm g toward Oc, also rotating the guest around the segment parallel to d e-to-e and crossing Oc. For each trial configuration, the potential energy was calculated, and the high-energy configurations were discarded. In all cases, the lowest energies were found for configurations of the adduct in which the guest points with the center of mass toward cm 1 . Although the adopted docking scheme for finding the initial relative arrangement of the adduct is rough and not necessarily exhaustive, reliable results were found for each guest species, as shown below.
In the third and last step, the potential energy profiles were calculated starting from the identified low-energy configurations while minimizing the energy with respect to the internal coordinates of the guest, the position of its center of mass cm g , and the rotations around its principal axes, while fixing the value of τ. Thus, the identified minima were approached starting from different initial configurations, making our simple approach quite reliable.
In Figure 4, the potential energy gained by the model dimer of PPO in the presence of αand β-form inducer guest molecules (ΔE) is shown as a function of τ. For each value of τ, the energy gain (ΔE) was calculated as the difference between the energy of the adduct with the stretched PPO model dimer E a-st and the sum (E g + E d-st ), that is, ΔE = E g-st − (E a + E d-st ). Therefore, the values of ΔE account exclusively for the dispersive energies established at the host-guest interface. The negative values of ΔE at a given τ value entail that the given conformation is stabilized by the guest. Notice that the lower the ΔE, the higher the stabilization effect.
It is apparent that by the effect of the presence of the guest molecules, a neat gain of potential energy is achieved, regardless of the τ value and guest type (Figure 4) (negative ΔE values). In particular, the β-form guest inducers DCA and CHCl 3 produce a neat decrease of the potential energy by 6.5-7.5 kcal/mol, whereas the α-form guest inducers TCA and CCl 4 produce a lower decrease of potential energy FIGURE 5 | Optimized structures of the low-energy configurations of the host-guest adducts obtained from calculations, for the βand α-forms inducers TCA and CCl 4 (top) and DCA and CHCl 3 (bottom), respectively. In addition, the ΔE values and the distance between CM 1 of the model dimer and the approximate guest center d CM1-guest are indicated for each host-guest adduct. The guest center is approximately located on the central carbon atom of the ball-like guests CCl 4 and CHCl 3 and the center of the C-C bond of TCA and DCA. The value of the valence angle τ is arbitrarily set equal to 130°. Similar configurations of the host-guest adducts would be obtained regardless of the value of τ. Legend: C of the guest and of the model dimer: light gray; O: red; Cl: green; H: empty spheres.
Frontiers in Chemistry | www.frontiersin.org January 2022 | Volume 9 | Article 809850 that amounts to 5-6 kcal/mol. Furthermore, whereas DCA and TCA tend to stabilize the stretched PPO conformations the higher, the greater the τ value, the potential energy stabilization tends to decrease for the ball-like molecules CCl 4 and CHCl 3 with increasing τ. Therefore, although kinetic aspects of the guest-induced crystallization of PPO in the αand β-forms come certainly into  The lowest and the highest values of the parameters were scaled to 100 and 0%, respectively, for ΔE and d CM1-guest , and to 0 and 100%, respectively, for the molecular volume and water solubility.
Frontiers in Chemistry | www.frontiersin.org January 2022 | Volume 9 | Article 809850 play, according to Figure 4, the stabilization of β-form essentially could be the result of a neat potential energy gain of the adducts with the DCA and CHCl 3 guest molecules, regardless of the stretching state of the model dimer.
The low-energy configurations of the host-guest adducts obtained from calculations for the αand β-form inducers are shown in Figure 5. For each host-guest adduct, the values of ΔE and of the distance between CM 1 of the model dimer and the approximate guest center d CM1-guest are also indicated in Figure 5. The guest center is approximately located on the central carbon atom of the ball-like guests CCl 4 and CHCl 3 and the center of the C-C bond of TCA and DCA. For the sake of simplicity, the model adducts of Figure 5 correspond to the configuration in which the value of the valence angle τ is arbitrarily set equal to 130°. Configurations similar to those shown in Figure 5, that is, with similar values of the d CM1-guest distances and not significant differences in energy gain ΔE, would be obtained also for host-guest adducts including the PPO model dimer in different conformations, regardless of the value of τ (data not shown).
Inspection of Figure 5 indicates that the β-form guest inducers CHCl 3 and DCA show a preferential interaction between a hydrogen atom and the center of the phenyl ring of the PPO dimer, while the αforms guest inducers CCl 4 and TCA preferentially interact via a chlorine atom with the center of the phenyl ring. Such a kind of interaction between a halogen atom and a phenyl ring has already been reported (Milano et al., 1998). Furthermore, the guests inducing the β-form show a shorter d CM1-guest distance than the guests inducing the α-form. In particular, the values of the host-guest distances d CM1guest are 3.6 and 3.3 Å for the β-form guest inducers DCA and CHCl 3 , respectively, and 4.5 and 4.4 Å for the α-form guest inducers TCA and CCl 4 , respectively. At the same time, the shorter distances d CM1-guest also reflect the tendency of the β-form inducers DCA and CHCl 3 to establish more favorable interactions with the PPO units, as the energy gain in terms of ΔE is higher than the one achieved by the α-form inducers TCA and CCl 4 (Figure 4).
In Table 4, the values of ΔE and d CM1-guest relative to the model adducts of Figure 5 are compared with the values of the leading parameters that have been identified in the preceding session (Tables 1-3) as the ones which control the formation of the CC and NC αand β-forms, that is, the water solubility and the volume of the molecule. The corresponding Kiviat diagrams are reported in Figure 6. The four axes of the Kiviat diagram correspond to the potential energy gain achieved by the PPO model dimer by the effect of the presence of the guests (ΔE), the host-guest center-to-center distance (d CM1-guest ), the guest molecular volume, and the water solubility of the guests. These parameters' lowest and highest values were scaled to 100 and 0%, respectively, for ΔE and d CM1-guest , and to 0 and 100%, respectively, for the molecular volume and water solubility.
The data of Figure 6 and Table 4 indicate that, in agreement with the data of Tables 1-3, more hydrophilic and smaller guest molecules favor the formation of the CC and NC crystalline β-form. Based on the potential energy calculations (Figures 4, 6B; Table 4), the β-form inducer guests are also those that establish highly favorable interactions with PPO units and form adducts with a low center-to-center distance (3.3-3.6 Å), at least in the case of DCA and CHCl 3 . The less hydrophilic guest molecules TCA and CCl 4 that possess a higher molecular volume, instead, ( Figure 6A) establish less favorable interactions with PPO units, form adducts with higher center-tocenter distance (4.4-4.5 Å), and thus favor the crystallization of α-form.

CONCLUSION
This study aimed to establish guest molecular features determining the formation of α or β CC and NC phases of PPO. This aim was pursued by collecting literature data and by adding many new film preparations (both by solution casting and by guest sorption in amorphous films) to evaluate the influence of the chemical nature of the guest on the formation of α or β phases.
The present analysis shows that independently of the two considered crystallization methods, the α-form is favored by hydrophobic and bulky guest molecules while the β-form (being characterized by a higher chain periodicity) is favored by hydrophilic and small guest molecules. In detail, all the considered guests with molecular volumes higher than 230 Å 3 and lower than 149 Å 3 lead to the αand β-forms, respectively. Moreover, all guests with solubility lower than 0.11 mmol per 100 ml of water and higher than 2 mmol per 100 ml of water lead to the αand βforms, respectively.
According to our molecular modeling study on two α-form inducer guests and on two β-form inducer guests, the latter would establish stronger dispersive interactions with the polymer chain than the α-form inducers. Therefore, the achievement of CC (and derived NC) β-forms would result from the high energy gain achieved by the adduct, and the short center-to-center distance established at hostguest interfaces.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, and further inquiries can be directed to the corresponding author.